133 lines
4.7 KiB
Python
133 lines
4.7 KiB
Python
import numpy as np
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import torch
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import torch.nn.functional as F
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def log_sum_exp(x):
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""" numerically stable log_sum_exp implementation that prevents overflow """
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# TF ordering
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axis = len(x.size()) - 1
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m, _ = torch.max(x, dim=axis)
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m2, _ = torch.max(x, dim=axis, keepdim=True)
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return m + torch.log(torch.sum(torch.exp(x - m2), dim=axis))
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# It is adapted from https://github.com/r9y9/wavenet_vocoder/blob/master/wavenet_vocoder/mixture.py
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def discretized_mix_logistic_loss(y_hat, y, num_classes=65536,
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log_scale_min=None, reduce=True):
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if log_scale_min is None:
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log_scale_min = float(np.log(1e-14))
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y_hat = y_hat.permute(0,2,1)
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assert y_hat.dim() == 3
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assert y_hat.size(1) % 3 == 0
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nr_mix = y_hat.size(1) // 3
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# (B x T x C)
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y_hat = y_hat.transpose(1, 2)
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# unpack parameters. (B, T, num_mixtures) x 3
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logit_probs = y_hat[:, :, :nr_mix]
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means = y_hat[:, :, nr_mix:2 * nr_mix]
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log_scales = torch.clamp(y_hat[:, :, 2 * nr_mix:3 * nr_mix], min=log_scale_min)
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# B x T x 1 -> B x T x num_mixtures
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y = y.expand_as(means)
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centered_y = y - means
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inv_stdv = torch.exp(-log_scales)
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plus_in = inv_stdv * (centered_y + 1. / (num_classes - 1))
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cdf_plus = torch.sigmoid(plus_in)
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min_in = inv_stdv * (centered_y - 1. / (num_classes - 1))
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cdf_min = torch.sigmoid(min_in)
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# log probability for edge case of 0 (before scaling)
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# equivalent: torch.log(F.sigmoid(plus_in))
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log_cdf_plus = plus_in - F.softplus(plus_in)
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# log probability for edge case of 255 (before scaling)
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# equivalent: (1 - F.sigmoid(min_in)).log()
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log_one_minus_cdf_min = -F.softplus(min_in)
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# probability for all other cases
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cdf_delta = cdf_plus - cdf_min
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mid_in = inv_stdv * centered_y
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# log probability in the center of the bin, to be used in extreme cases
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# (not actually used in our code)
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log_pdf_mid = mid_in - log_scales - 2. * F.softplus(mid_in)
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# tf equivalent
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"""
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log_probs = tf.where(x < -0.999, log_cdf_plus,
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tf.where(x > 0.999, log_one_minus_cdf_min,
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tf.where(cdf_delta > 1e-5,
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tf.log(tf.maximum(cdf_delta, 1e-12)),
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log_pdf_mid - np.log(127.5))))
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"""
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# TODO: cdf_delta <= 1e-5 actually can happen. How can we choose the value
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# for num_classes=65536 case? 1e-7? not sure..
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inner_inner_cond = (cdf_delta > 1e-5).float()
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inner_inner_out = inner_inner_cond * \
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torch.log(torch.clamp(cdf_delta, min=1e-12)) + \
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(1. - inner_inner_cond) * (log_pdf_mid - np.log((num_classes - 1) / 2))
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inner_cond = (y > 0.999).float()
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inner_out = inner_cond * log_one_minus_cdf_min + (1. - inner_cond) * inner_inner_out
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cond = (y < -0.999).float()
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log_probs = cond * log_cdf_plus + (1. - cond) * inner_out
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log_probs = log_probs + F.log_softmax(logit_probs, -1)
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if reduce:
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return -torch.mean(log_sum_exp(log_probs))
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else:
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return -log_sum_exp(log_probs).unsqueeze(-1)
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def sample_from_discretized_mix_logistic(y, log_scale_min=None):
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"""
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Sample from discretized mixture of logistic distributions
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Args:
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y (Tensor): B x C x T
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log_scale_min (float): Log scale minimum value
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Returns:
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Tensor: sample in range of [-1, 1].
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"""
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if log_scale_min is None:
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log_scale_min = float(np.log(1e-14))
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assert y.size(1) % 3 == 0
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nr_mix = y.size(1) // 3
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# B x T x C
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y = y.transpose(1, 2)
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logit_probs = y[:, :, :nr_mix]
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# sample mixture indicator from softmax
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temp = logit_probs.data.new(logit_probs.size()).uniform_(1e-5, 1.0 - 1e-5)
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temp = logit_probs.data - torch.log(- torch.log(temp))
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_, argmax = temp.max(dim=-1)
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# (B, T) -> (B, T, nr_mix)
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one_hot = to_one_hot(argmax, nr_mix)
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# select logistic parameters
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means = torch.sum(y[:, :, nr_mix:2 * nr_mix] * one_hot, dim=-1)
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log_scales = torch.clamp(torch.sum(
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y[:, :, 2 * nr_mix:3 * nr_mix] * one_hot, dim=-1), min=log_scale_min)
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# sample from logistic & clip to interval
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# we don't actually round to the nearest 8bit value when sampling
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u = means.data.new(means.size()).uniform_(1e-5, 1.0 - 1e-5)
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x = means + torch.exp(log_scales) * (torch.log(u) - torch.log(1. - u))
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x = torch.clamp(torch.clamp(x, min=-1.), max=1.)
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return x
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def to_one_hot(tensor, n, fill_with=1.):
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# we perform one hot encore with respect to the last axis
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one_hot = torch.FloatTensor(tensor.size() + (n,)).zero_()
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if tensor.is_cuda:
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one_hot = one_hot.cuda()
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one_hot.scatter_(len(tensor.size()), tensor.unsqueeze(-1), fill_with)
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return one_hot
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